Computing derangement probabilities of the symmetric group acting on k-sets

Abstract

Let $i(\infty ,k)$ be the limiting proportion, as $n\to \infty$, of permutations in the symmetric group of degree $n$ that fix a $k$-set. We give an algorithm for computing $i(\infty ,k)$ and state the values of $i(\infty ,k)$ for $k\le 30$. These values are consistent with a conjecture of Peter Cameron that $i(\infty ,k)$ is a decreasing function of $k$.

9 pages, 1 figure

Cited by in corpus (1)

• Permutations fixing a k-set